Pls help me with these problem solving sums
-----------------------------------------
1)You are building a rectangular brick patio surrounded by crushed stone in a rectangular courtyard.The crushed stone border has a uniform width x (in feet) you have enough money in your budget to purchase patio bricks to cover 140 sq.feet solve the equation 140=(20-2x)(16-2x) to find the width of the border
2) The distance d (in feet) that it takes a car to come to a complete stop on dry asphalt can be modeled by d=0.05+1.1s where s is the speed of the car (in miles per hour).A car has 78 feet to come to a complete stop. Find the max. Speed at which the car can travel
thanks this helped 6 years later during coronavirus outbreak. online school sucks.
1) The border is 3 Feet
bro i think we in the same math class Joe Mama i had this same problem the same day is your teacher Ms Grimaldo?
1) Sure, let's solve the first problem together. We need to find the width of the border, represented by "x".
We have the equation 140 = (20-2x)(16-2x).
To simplify the equation, let's first distribute the terms:
140 = (320 - 40x - 32x + 4x^2).
Next, combine like terms:
140 = 4x^2 - 72x + 320.
Now, rearrange the equation to form a quadratic equation:
4x^2 - 72x + 320 - 140 = 0.
Simplify the equation further:
4x^2 - 72x + 180 = 0.
Divide the equation by 4 to simplify:
x^2 - 18x + 45 = 0.
Now let's solve this quadratic equation using factoring or the quadratic formula. I'll use factoring for simplicity:
Factor the quadratic equation:
(x - 5)(x - 9) = 0.
Now set each factor equal to zero and solve for x:
x - 5 = 0 or x - 9 = 0.
Solving for x gives us:
x = 5 or x = 9.
Therefore, the width of the border can be either 5 feet or 9 feet.
2) Now let's solve the second problem. We are given the equation d = 0.05 + 1.1s, where d represents the distance in feet and s represents the speed in miles per hour.
We need to find the maximum speed at which the car can travel with 78 feet to come to a complete stop.
Plug in the given values into the equation:
78 = 0.05 + 1.1s.
Subtract 0.05 from both sides of the equation:
77.95 = 1.1s.
Divide both sides of the equation by 1.1:
77.95/1.1 = s.
Simplifying this gives us:
70.86 ≈ s.
So, the maximum speed at which the car can travel is approximately 70.86 miles per hour.
I hope that helps! Let me know if you have any more questions or if you need a good joke to lighten the mood.
Sure, let's solve these problem-solving sums step by step:
1) To find the width of the border in the rectangular courtyard, we need to solve the equation: 140 = (20 - 2x)(16 - 2x).
To solve this equation, we can expand it, simplify, and then solve for x:
140 = (20 - 2x)(16 - 2x)
140 = 320 - 72x + 4x^2
Rearrange the equation to form a quadratic equation:
4x^2 - 72x + 320 - 140 = 0
4x^2 - 72x + 180 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's solve it using factoring:
4x^2 - 72x + 180 = 0
Divide through by 4 to simplify the equation:
x^2 - 18x + 45 = 0
Now we factor this equation:
(x - 3)(x - 15) = 0
So we have two possible values for x: x = 3 or x = 15.
Therefore, the width of the border can be either 3 feet or 15 feet.
2) The equation given is: d = 0.05 + 1.1s
We are given that the distance, d, is 78 feet. We need to find the maximum speed, s, at which the car can travel.
Substitute the value of d into the equation to solve for s:
78 = 0.05 + 1.1s
Rearrange the equation to isolate s:
1.1s = 78 - 0.05
1.1s = 77.95
Divide both sides by 1.1 to solve for s:
s = 77.95 / 1.1
Using a calculator, we can calculate s using the above expression. After evaluation, we find that:
s ≈ 70.86
Therefore, the maximum speed at which the car can travel is approximately 70.86 miles per hour.